Sound-Horizon-Independent Test of Cosmic Distance Duality Relation Using Artificial Neural Networks and Gaussian Processes

Abstract

The cosmic distance duality relation (CDDR), $D_L(z)(1+z)^{-2}/D_A(z) \equiv 1$, is a fundamental relation in modern cosmology linking luminosity distance $D_L$ and angular diameter distance $D_A$. We define $η(z) \equiv D_L(z)(1+z)^{-2}/D_A(z)$ and reconstruct the relevant quantities over $0 < z < 2.5$ using two independent non-parametric methods: Gaussian processes (GP) and artificial neural networks (ANN). Specifically, we reconstruct $D_L$ from three different Type Ia supernovae (SNe$~$Ia) compilations (PantheonPlus, Union3, and DES-Dovekie), the baryon acoustic oscillation distance ratio $D_M/D_H$ from SDSS and DESI, and the Hubble function $H(z)$ from cosmic chronometer (CC) data. Our CDDR test is independent of both the cosmological model and the sound horizon $r_d$ calibration, as $D_M/D_H$ naturally eliminates $r_d$. We render our GP reconstructions insensitive to mean-function and kernel choices via full Bayesian marginalization over hyperparameters, with ANN as a cross-check$-$revealing the impact of data sparsity on the latter. Our results show no significant deviation from the CDDR exceeding $2σ$, and for the CC+BAO+DES-Dovekie combination it remains within $1σ$ over most of the redshift range. With $r_d$ eliminated, varying the only remaining external parameter $M_B$ systematically shifts $η(z)$ through the $M_B$-$H_0$ degeneracy, indicating that the observed $η\neq1$ signal is closely tied to $H_0$ tension among datasets and is likely driven by $M_B$ systematics rather than a true CDDR violation. Future high-quality CC, BAO, and SNe$~$Ia data$-$with either improved $M_B$ calibration or $M_B$-free distance measurements$-$will be essential for extending this calibration-free approach.